Paweł Błażej

The role of crossover operator in evolutionary-based approach to the problem of genetic code optimization

One of theories explaining the present structure of canonical genetic code assumes that it was optimized to minimize harmful effects of amino acid replacements resulting from nucleotide substitutions and translational errors. A way to testify this concept is to find the optimal code under given criteria and compare it with the canonical genetic code. Unfortunately, the huge number of possible alternatives makes it impossible to find the optimal code using exhaustive methods in sensible time. Therefore, heuristic methods should be applied to search the space of possible solutions. Evolutionary algorithms (EA) seem to be ones of such promising approaches. This class of methods is founded both on mutation and crossover operators, which are responsible for creating and maintaining the diversity of candidate solutions. These operators possess dissimilar characteristics and consequently play different roles in the process of finding the best solutions under given criteria. Therefore, the effective searching for the potential solutions can be improved by applying both of them, especially when these operators are devised specifically for a given problem. To study this subject, we analyze the effectiveness of algorithms for various combinations of mutation and crossover probabilities under three models of the genetic code assuming different restrictions on its structure. To achieve that, we adapt the position based crossover operator for the most restricted model and develop a new type of crossover operator for the more general models. The applied fitness function describes costs of amino acid replacement regarding their polarity. Our results indicate that the usage of crossover operators can significantly improve the quality of the solutions. Moreover, the simulations with the crossover operator optimize the fitness function in the smaller number of generations than simulations without this operator. The optimal genetic codes without restrictions on their structure minimize the costs about 2.7 times better than the canonical genetic code. Interestingly, the optimal codes are dominated by amino acids characterized by polarity close to its average value for all amino acids.

Optimization of Mutation Pressure in Relation to Properties of Protein-Coding Sequences in Bacterial Genomes

Most mutations are deleterious and require energetically costly repairs. Therefore, it seems that any minimization of mutation rate is beneficial. On the other hand, mutations generate genetic diversity indispensable for evolution and adaptation of organisms to changing environmental conditions. Thus, it is expected that a spontaneous mutational pressure should be an optimal compromise between these two extremes. In order to study the optimization of the pressure, we compared mutational transition probability matrices from bacterial genomes with artificial matrices fulfilling the same general features as the real ones, e.g., the stationary distribution and the speed of convergence to the stationarity. The artificial matrices were optimized on real protein-coding sequences based on Evolutionary Strategies approach to minimize or maximize the probability of non-synonymous substitutions and costs of amino acid replacements depending on their physicochemical properties. The results show that the empirical matrices have a tendency to minimize the effects of mutations rather than maximize their costs on the amino acid level. They were also similar to the optimized artificial matrices in the nucleotide substitution pattern, especially the high transitions/transversions ratio. We observed no substantial differences between the effects of mutational matrices on protein-coding sequences in genomes under study in respect of differently replicated DNA strands, mutational cost types and properties of the referenced artificial matrices. The findings indicate that the empirical mutational matrices are rather adapted to minimize mutational costs in the studied organisms in comparison to other matrices with similar mathematical constraints.

The Impact of Selection at the Amino Acid Level on the Usage of Synonymous Codons

There are two main forces that affect usage of synonymous codons: directional mutational pressure and selection. The effectiveness of protein translation is usually considered as the main selectional factor. However, biased codon usage can also be a byproduct of a general selection at the amino acid level interacting with nucleotide replacements. To evaluate the validity and strength of such an effect, we superimposed >3.5 billion unrestricted mutational processes on the selection of nonsynonymous substitutions based on the differences in physicochemical properties of the coded amino acids. Using a modified evolutionary optimization algorithm, we determined the conditions in which the effect on the relative codon usage is maximized. We found that the effect is enhanced by mutational processes generating more adenine and thymine than guanine and cytosine, as well as more purines than pyrimidines. Interestingly, this effect is observed only under an unrestricted model of nucleotide substitution, and disappears when the mutational process is time-reversible. Comparison of the simulation results with data for real protein coding sequences indicates that the impact of selection at the amino acid level on synonymous codon usage cannot be neglected. Furthermore, it can considerably interfere, especially in AT-rich genomes, with other selections on codon usage, e.g., translational efficiency. It may also lead to difficulties in the recognition of other effects influencing codon bias, and an overestimation of protein coding sequences whose codon usage is subjected to adaptational selection.

Optimization of amino acid replacement costs by mutational pressure in bacterial genomes

Mutations are considered a spontaneous and random process, which is important component of evolution because it generates genetic variation. On the other hand, mutations are deleterious leading to non-functional genes and energetically costly repairs. Therefore, one can expect that the mutational pressure is optimized to simultaneously generate genetic diversity and preserve genetic information. To check if empirical mutational pressures are optimized in these ways, we compared matrices of nucleotide mutation rates derived from bacterial genomes with their best possible alternatives that minimized or maximized costs of amino acid replacements associated with differences in their physicochemical properties (e.g. hydropathy and polarity). It should be noted that the studied empirical nucleotide substitution matrices and the costs of amino acid replacements are independent because these matrices were derived from sites free of selection on amino acid properties and the amino acid costs assumed only amino acid physicochemical properties without any information about mutation at the nucleotide level. Obtained results indicate that the empirical mutational matrices show a tendency to minimize costs of amino acid replacements. It implies that bacterial mutational pressures can evolve to decrease consequences of amino acid substitutions. However, the optimization is not full, which enables generation of some genetic variability.

Using evolutionary algorithms in finding of optimized nucleotide substitution matrices

Mutations occurring in biological DNA sequences are not completely random but are a result of coevolution between mutational pressure with selection constraints around the genetic code [2, 5] and can be optimized to some extent during evolution ([6]). On one hand, most mutations are deleterious and generate energetic costs of their repairing, therefore a tendency to decrease the mutation rate should exist. On the other hand, mutations are responsible for genetic diversity, which is necessary for adaptation in changing environment. Therefore, an elevated level of mutation rate should be also expected in these cases. It indicates that the real mutational pressure should be subjected to some optimization in biological systems.

Representations of Search Spaces in the Problem of Mutational Pressure Optimization According to Protein-Coding Sequences

The proper representation of the search space is the fundamental step in every optimization task, because it has a decisive impact on the quality of potential solutions. In particular, this problem appears when the search spaces are nonstandard and complex, with the large number of candidate solutions that differ from classical forms usually investigated. One of such spaces is the set of continuous-time, homogenous, and stationary Markov processes. They are commonly used to describe biological phenomena, for example, mutations in DNA sequences and their evolution. Because of the complexity of these processes, the representation of their search space is not an easy task but it is important for effective solving of the biological problems. One of them is optimality of mutational pressure acting on protein-coding sequences. Therefore, we described three representations of the search spaces and proposed several specific evolutionary operators that are used in evolutionary-based optimization algorithms to solve the biological problem of mutational pressure optimality. In addition, we gave a general formula for the fitness function, which can be used to measure the quality of potential solutions. The structures of these solutions are based on two models of DNA evolution described by substitution-rate matrices, which are commonly used in phylogenetic analyzes. The proposed representations have been successfully utilized in various issues, and the obtained results are very interesting from a biological point of view. For example, they show that mutational pressures are, to some extent, optimized to minimize cost of amino acid substitutions in proteins.

The Importance of Changes Observed in the Alternative Genetic Codes

The standard genetic code is a way of transmitting genetic information from DNA into protein world. The code is universal for almost all living organisms on Earth but small deviations have been observed for many cellular organelles and some specific groups of microorganisms with highly reduced genomes. Such modifications are called alternative genetic codes. There is no consensus about the factors that caused or allowed these changes. A popular concept assumes that the codes evolved under neutral evolution without adaptive constraints. In this paper we present findings that argue with such view. We examined the level of error minimization in amino acid replacements generated by the standard genetic code and its alternatives. We found that only 3 out of 23 tested alternative codes have worse quality than the standard genetic code. In agreement with that, many single codon reassignments observed in the variants of the standard genetic code are generally responsible for improving the quality of the codes under the studied criteria. These results indicate that the codon reassignments observed in the existing alternative genetic codes could play an adaptive role in their evolution to minimize translational and mutational errors. The study can help in designing alternative genetic codes for artificially modified organisms in the framework of synthetic biology.

The structure of the genetic code as an optimal graph clustering problem

The standard genetic code (SGC) is the set of rules by which genetic information is translated into proteins, from codons, i.e. triplets of nucleotides, to amino acids. The questions about the origin and the main factor responsible for the present structure of the code are still under a hot debate. Various methodologies have been used to study the features of the code and assess the level of its potential optimality. Here, we introduced a new general approach to evaluate the quality of the genetic code structure. This methodology comes from graph theory and allows us to describe new properties of the genetic code in terms of conductance. This parameter measures the robustness of codon groups against the potential changes in translation of the protein-coding sequences generated by single nucleotide substitutions. We described the genetic code as a partition of an undirected and unweighted graph, which makes the model general and universal. Using this approach, we showed that the structure of the genetic code is a solution to the graph clustering problem. We presented and discussed the structure of the codes that are optimal according to the conductance. Despite the fact that the standard genetic code is far from being optimal according to the conductance, its structure is characterised by many codon groups reaching the minimum conductance for their size. The SGC represents most likely a local minimum in terms of errors occurring in protein-coding sequences and their translation.

Role of recombination and faithfulness to partner in sex chromosome degeneration

Sex determination in mammals is strongly linked to sex chromosomes. In most cases, females possess two copies of X chromosome while males have one X and one Y chromosome. It is assumed that these chromosomes originated from a pair of homologous autosomes, which diverged when recombination between them was suppressed. However, it is still debated why the sex chromosomes stopped recombining and how this process spread out over most part of the chromosomes. To study this problem, we developed a simulation model, in which the recombination rate between the sex chromosomes can freely evolve. We found that the suppression of recombination between the X and Y is spontaneous and proceeds very quickly during the evolution of population, which leads to the degeneration of the Y in males. Interestingly, the degeneration happens only when mating pairs are unfaithful. This evolutionary strategy purifies the X chromosome from defective alleles and leads to the larger number of females than males in the population. In consequence, the reproductive potential of the whole population increases. Our results imply that both the suppression of recombination and the degeneration of Y chromosome may be associated with reproductive strategy and favoured in polygamous populations with faithless mating partners.

The influence of habitat preferences on shell morphology in ecophenotypes of Trochulus hispidus complex

Trochulus hispidus and T. sericeus are hairy snails widely distributed in Europe. They differ in shell morphology and are usually found in various land habitats. However, their morphology does not match genetic distance as they do not form distinct clades. Therefore, it is interesting to determine to what extent environmental factors can control their phenotypes. We analysed the morphological traits and many environmental features of their habitats to find relationships between these parameters and explain ecological reasons for this plasticity. We found many statistically significant correlations between morphological traits and environmental variables. Illumination, forestation, precipitation and temperature occurred the most important features discriminating habitats of these snails. It turned out that T. sericeus prefers forests and moist shaded places, while T. hispidus chooses more dry habitats and open areas exposed to the sun. T. sericeus is also probably more tolerant to low and variable temperatures. The hair durability is also correlated with their habitats: the shell of T. hispidus is mostly hairless but hairs almost always cover the shell of T. sericeus. These results support the hypothesis that the lack of hairs is associated with the loss of a potential adaptive function due to the change from wet to dry habitats. The hairs facilitate the adherence of snails to herbaceous plants during feeding when the humidity levels are high. The morphological divergence of T. hispidus and T. sericeus is the result of phenotypic plasticity and selection associated with the habitat, which affect both the shell shape and the hair durability. Since T. hispidus and T. sericeus do to not represent separate biological species and their variability has no genetic basis, they should be considered as ecophenotypes. This and our previous studies suggest that phenotypic plasticity in widely distributed Trochulus species is quite common and may have been of ancestral origin.